X-rays used in a CT apparatus and the like do not have single energy, but are polychromatic X-rays which are a mixture of X-rays with various energies. Generally, X-rays with low energy attenuate easily through an interaction with a transmission substance, compared with X-rays with high energy. Therefore, with progress of transmission through a substance, an energy distribution of X-rays tends to show a high energy side remaining, which does not easily attenuate. As a result, an attenuation coefficient for polychromatic X-rays is not constant, but gradually becomes small. Such phenomenon is called “beam hardening phenomenon”.
FIG. 7 is a graph schematically showing a correlation between the length of a transmission substance (hereinafter abbreviated as “transmission length”) and the X-ray detection signal ratio between pre-transmission and post-transmission (hereinafter defined as “quantity of attenuation”). In FIG. 7, the horizontal axis represents transmission length K while the vertical axis with a logarithmic scale represents the quantity of attenuation. Monochromatic X-rays describe a straight line as shown in a dotted line in FIG. 7 since detection signal values are expressed by an exponential function having the transmission length K as the variable. It is seen, however, that polychromatic X-rays describe a curve which extends in a direction of the less attenuation resulting from the longer transmission length K as shown in a solid line in FIG. 7.
Generally, in CT reconstruction, a transmission length is converted from attenuation (that is, the quantity of attenuation) of detection signal values, and a distribution of transmission substances is obtained by solving an inverse problem. If a transmission length is calculated based on a consideration that attenuation is fixed without taking the beam hardening phenomenon into consideration, the transmission length cannot be calculated accurately. And CT reconstruction images will have, appearing thereon, artifacts due to a cupping phenomenon, for example, in which CT values lower in the central parts of the reconstruction images. Therefore, the beam hardening phenomenon must be taken into consideration when converting attenuation of the detection signal values into a transmission length.
There is a technique of preparing beforehand a function that can convert attenuation of transmission signal values into a transmission length of a transmission substance, in which the X-ray transmission length of the transmission substance is changed variously, and attenuation of each detection signal value is measured to be used as a basis. Specifically, where P0 is a detection signal value before attenuation (that is, a detection signal value before transmission) corresponding to zero transmission length of the transmission substance, and P is a detection signal value after transmission, the quantity of attenuation is P/P0 based on the above definitions, and an attenuation value Ln is derived from a definition Ln=−ln(P/P0). In is a natural logarithmic function. Using attenuation values measured when the transmission length is changed variously, and an inverse function is obtained beforehand as approximate function.
There is also a technique of correcting beam hardening, which adjusts a detection signal energy distribution of a system by measuring data of two phantoms and adjusting transmission lengths of two filters (see Patent Document 1, for example).
[Patent Document 1]
Specification of United States Patent Application Publication No. 2005/0013414